What is a recursive formula for a geometric sequence?

1 Answer
Oct 28, 2016

Answer:

Recursive formula for a geometric sequence is #a_n=a_(n-1)xxr#, where #r# is the common ratio.

Explanation:

A geometric series is of the form

#a,ar,ar^2,ar^3,ar^4,ar^5.........................#

in which first term #a_1=a# and other terms are obtained by multiplying by #r#.

Observe that each term is #r# times the previous term. Hence to get #n^(th)# term we multiply #(n-1)^(th)# term by #r#

i.e. #a_n=a_(n-1)xxr#

This is called recursive formula for geometric sequence.

There is also explicit formula for #n^(th)# term i.e. #a_n=axxr^(n-1)#